Physics 1602 8

1. Consider a scalar space ψ.

• ψ and ψ’ represent the same 4-vector input regardless of the frame.
• (Of course, if it’s a different frame, it’s a different event, but we won’t consider that here.)

2. Relate the position dependence of the fields between the two frames.

• It is important not to mix up these issues.

• The surface charge density is equal to ρ times d.

  • If we boost in the direction perpendicular to the surface, ρ will change but d will remain constant.

• $E_{||}^{\prime }=\gamma E_{||P}$

  • E, which is proportional to the density (e.g. σ/2ε_0), is not a 4-vector.
  • The component in the boost direction is invariant.

• There are cases where ρ=0 and J=0.

  • J=0 means there is charge but the velocity is zero.
  • ρ=0 refers to something magnetic.

• Transformation of Gauss’s law

  • The partial derivative interacts with the Lorentz contact and introduces a γ factor.

• Towards the end

  • I want to verify the conditions ∇・E = 0 and J = 0.